State Charles' law and identify which variables are held constant.

State Charles' law and identify which variables are held constant.

• A. P ∝ V at constant n and T; P1V1 = P2V2.
• B. V ∝ T at constant P and n; V1/T1 = V2/T2.
• C. V ∝ P at constant n and T; V1/P1 = V2/P2.
• D. V ∝ T at constant n and P; V1/T1 = V2/T2 with temperatures in Kelvin.

Answer: (D)

Charles' law shows that at a fixed amount of gas and fixed pressure, the volume changes directly with the absolute temperature. In other words, V is proportional to T when P and n are constant, so comparing two states gives V1/T1 = V2/T2. Because temperature must be on an absolute scale, the temperatures need to be in Kelvin for the relationship to hold. This option correctly states V ∝ T at constant n and P and uses V1/T1 = V2/T2 with temperatures in Kelvin. The other statements either mix in the wrong variables (for example, relating P to V or V to P), which describe different gas laws, or omit the requirement to use Kelvin, which is essential for the proportionality to be valid.

Charles' law shows that at a fixed amount of gas and fixed pressure, the volume changes directly with the absolute temperature. In other words, V is proportional to T when P and n are constant, so comparing two states gives V1/T1 = V2/T2. Because temperature must be on an absolute scale, the temperatures need to be in Kelvin for the relationship to hold.

This option correctly states V ∝ T at constant n and P and uses V1/T1 = V2/T2 with temperatures in Kelvin. The other statements either mix in the wrong variables (for example, relating P to V or V to P), which describe different gas laws, or omit the requirement to use Kelvin, which is essential for the proportionality to be valid.